People want to filter out lolis and shotas or look for them but people generally aren't bothered by the presence of lackthereof of a child.
This makes me think of a reference/clip, particularly as you bolded the word
-
"There's only one thing worse than a rapist - a __"
As for the tag, I think it's a good idea. Maybe not the proposed name, but it is definitely a subgenre with some population and interest. (Though I am unsure where story's like the 's-ranked daughter' and '4 orphans moved out into a city and love their adoptive father romantically' would place in relation to it, as they are very adjacent but not quite there... Well, maybe not the latter once you gotten 2 chapters in, but before then kinda)
As for alternative names, I used to call it rearing or grooming before (the latter because I know it annoys ppl while still being entirely technically correct - the best kind of correct), but then I saw a korean manwha (transmigrators privilege?) that explained it's an already established genre named "romfam" (for "romance family", interestingly enough
not referring to incest according to that manwha, despite it's name entirely suggesting such).
Searching for it on google before never netted me any results, so might just be the translator doing a real poor job at translating a korean 'name' (likely directly translated)... But in that case I am just even more hyped to use that name, because it's so incorrect because someone erred
So either way I would nominate that name for the genre:
"romfam".
edit: went back and checked, apparently it was "rofan" for "romance fantasy". Making rofam even more incorrect (Because I were incorrect when spelling it + not only is rofan not even including family in title despite being about childcare, it's suggesting there is regular romance in the fantasy story despite it not being about romance!), and thus even better of a candidate!
Technically the full name described in the manwha was "rofan childcare", but at times it was abbreviated to rofan, and childcare is a mouthful.